Question

Potato chips A company that makes potato chips requires each shipment of

potatoes to meet certain quality standards. If the company finds convincing evidence that more than $8\%$of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of $H_0:p=0.08$versus $H_a:p>0.08$, where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that $p=0.11$, based on a random sample of $500$ potatoes and significance level $\alpha =0.05$, is $0.764$Interpret this value.

Short answer

There is sufficient evidence to favor the alternative hypothesis, that is, $H_0:p>0.08$

Step-by-step solution

Given information

Hypothesized population proportion $\left(p0\right)=0.08$

Sample size $\left(n\right)=500$

Level of significance $\left(\alpha \right)=0.05$

Power = 0.764

The null and alternative hypotheses are:

$$\begin{gathered} H_0:p=0.08 \\ {H}_a:p>0.08 \end{gathered}$$

Concept

The likelihood of rejecting the null hypothesis if the alternative hypothesis is true is defined as the test's power.

Explanation

The test's power of $0.764$ indicates that there is a $76.4$ percent chance of concluding that there is adequate evidence to support the alternative hypothesis, $H_0:p>0.08$